Question

A ball of mass $500\text{g}$ is initially at rest at the bottom most point of a smooth vertical circular track of radius $10\text{m}$. For looping a loop, the minimum kinetic energy the ball should have at the bottommost point on the track is

• A. $100\text{J}$
• B. $125\text{J}$
• C. $250\text{J}$
• D. $1250\text{J}$

Answer 1

The correct option is B $125\text{J}$

Let the velocity of the ball at the bottom of the track be $v_A$

The minimum velocity at the bottom for completing the loop is given by,
$v_{\text{bottom}}=v_A=\sqrt{5gl}$

$\Rightarrow v_A=\sqrt{5\times 10\times 10}=10\sqrt{5}\text{m/s}$

Hence the minimum kinetic energy at the bottom most point on the track is given by,
$\text{K.E}=\frac{1}{2}m{v}_A^2=\frac{1}{2}\times 0.5\times (100\times 5)$

$\Rightarrow \text{K.E}=125\text{J}$

Hence option B is the correct answer.